I discovered today that FaceTime didn’t work on my iPhone 4: people couldn’t start FaceTime calls with me and I didn’t have any of the FaceTime buttons present. Turns out that this problem is caused when restoring from an iPhone 3G running iOS 4 — it seems the FaceTime on/off setting is imported from the iPhone 3G (which has it turned off as it doesn’t support FaceTime). Going into Settings > Phone and then flipping FaceTime on solved it for me.
Other people seem to have had to jump through a couple of extra hoops to get this to work, if flipping the switch didn’t get you going, take a look at this post over at the Rusty Brick blog.
Update 2010-08-22: Still having trouble? Did you jailbreak your iPhone 4? There’s something else that might stop this working too.
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Update 2012-07-18: Several people have reported that the FaceTime icon disappears after you have done the initial setup, and that this is normal. To make a FaceTime call once setup is complete, go into your Contacts, find the person you want to video chat with, then you should see a FaceTime button underneath their contact info, in the same ara that the “Text Message” button is. Thanks to everyone who’s commented for sharing their stories!